Multiscale estimation of the Freundlich adsorption isotherm

Abstract

ABSTRACT:Adsorption plays an important role in water and wastewater treatment. The analysis and design of processes that involve adsorption rely on the availability of isotherms that describe these adsorption processes. Adsorption isotherms are usually estimated empirically from measurements of the adsorption process variables. Unfortunately, these measurements are usually contaminated with errors that degrade the accuracy of estimated isotherms. Therefore, these errors need to be filtered for improved isotherm estimation accuracy. Multiscale wavelet based filtering has been shown to be a powerful filtering tool. In this work, multiscale filtering is utilized to improve the estimation accuracy of the Freundlich adsorption isotherm in the presence of measurement noise in the data by developing a multiscale algorithm for the estimation of Freundlich isotherm parameters. The idea behind the algorithm is to use multiscale filtering to filter the data at different scales, use the filtered data from all scales to construct multiple isotherms and then select among all scales the isotherm that best represents the data based on a cross validation mean squares error criterion. The developed multiscale isotherm estimation algorithm is shown to outperform the conventional time-domain estimation method through a simulated example.

Effect of the Pyrrolic Nitrogen Functional Group in the Selective Adsorption of CO2: GCMC, MD, and DFT Studies

“…Although the two models mentioned above have a wide range of applications for different systems, the combination of these models is more popular due to the fact that each model has some drawbacks. , On the other hand, the Langmuir–Freundlich model properly considers the heterogeneity of the adsorbent as presented in the following equation …”

“…where k is the constant of the Freundlich model and n determines the extent of heterogeneity of the surface of the adsorbent as the higher value of n (n > 1) for adsorption illustrates that the adsorbate can favorably attach on the Although the two models mentioned above have a wide range of applications for different systems, the combination of these models is more popular due to the fact that each model has some drawbacks. 47,48 On the other hand, the Langmuir− Freundlich model properly considers the heterogeneity of the adsorbent as presented in the following equation…”

Adsorption and desorption of three carbamate pesticides by illite, kaolinite and humic acid-clay complexes

“…The results from Freundlich equation fittings are given in Table 1. The value of 1/n during adsorption of three carbamate pesticides on Na-and Casaturated illite and kaolinite were less than unity indicating a convex or 'L' type of isotherm [17,18] [Fig 1a and 1b] and were higher for illite than kaolinite. This kind of isotherm may arise because of minimum competition of solvent for sites on the adsorbing surface.…”

Simultaneous spectrophotometric determination of phosphate and silicate in different water and soil samples using chemometrics approach

“…However, conventional spectrophotometric methods yield poor results for quantitative analysis of multi-component mixtures due to overlapping absorption spectra in the same spectral region. Therefore, the representation of a signal by means of its spectrum or Fourier transform is essential for solving mentioned problems in different science (Nounou and Nounou 2010;Rajaee et al 2010;Jalalkamali et al 2015).…”